In a game, you have the following:

Conditions

A player can choose at most K coins one by one.
They cannot choose a value that is present in the list of restricted coins.
At the beginning of the game, the list of restricted coins is empty. Whenever a player selects a coin, it is added to their profit and also appended in the list of restricted coins.
A player can discard a coin even if it is not present in the list of restricted coins.

Task

Your task is to determine the maximum profit that a player can make.

Input format

Output format

For each test case, print a single line denoting the maximum profit a player can make.

Constraints